Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30135
Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising

Authors: Jianwei Ma, Diriba Gemechu

Abstract:

In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.

Keywords: Anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, Split Bregman Algorithm.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1315601

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 477

References:


[1] W. Lu et al., 2016. Implementation of high-order variational models made easy for image processing. Mathematical Methods in the Applied Science. DOI: 10.1002/mma.3858.
[2] Weickert, J., 1998. Anisotropic Diffusion in Image Processing. B.G. Teub-ner, Stuttgart.
[3] Perona, P., Malik, J., 1990. Scale-space and edge-detection using anisotropic diffusion. IEEE Transact. Pattern Anal. Mach. Intell. 12 (7), 629639.
[4] Rudin, L., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Phys. D 60, 259268.
[5] Chan, T. F., Shen, J. H., 2005. Image Processing and Analysis: Variational, PDE,Wavelet, and Stochastic Methods. SIAM: Philadelphia, USA, 2005.
[6] Aubert, G., Kornprobst, P., 2006. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer Science and Business Media: New York, USA, 2006,147.
[7] Paragios, N., Chen, Y. M., 2011. Faugeras O. Handbook of Mathematical Models in Computer Vision. Springer Science and Business Media: New York, USA, 2006. Scherzer O. Handbook of Mathematical Methods in Imaging. Springer Science and Business Media: New York, USA, 2011,1.
[8] Chen, F., Li, J. Z., Huang, J. M., Li, D. D., 2003. Application research of digital image processing method for improving signal to noise ration of seismic section image. Prog. Geophys. 18 (4), 758764.
[9] Wang, D., Gao, J., 2014. A new method for random noise attenuation in seismic data based on anisotropic fractional-gradient operators. J. Appl. Geophys. 110 (2014), 135143.
[10] D. Gemechu et al., 2017. Random noise attenuation using an improved anisotropic total variation regularization. J. Appl. Geophys. 144 (2017) 173-187.
[11] Lavialle, O., Pop, S., Germain, C., Donias, M., Guillon, S., Keskes, N., Berthoumieu, Y., 2007. Seismic fault preserving diffusion. J. Appl. Geophys. 61, 132141.
[12] Qu, Y., Cao, J. X., Zhu, H. D., Ren, C., 2011. An improved total variation technique for seismic image denoising. Acta Petrol. Sin. 32 (5), 815819.
[13] Wang, X. S., Yang, C. C., 2006. An edge preserving smoothing algorithm of seismic image using nonlinear anisotropic diffusion equation. Prog. Geophys. 21 (2), 452457.
[14] Lari, H. H., Gholami, A., 2014. Curvelet-TV regularized Bregman iteration for seismic random noise attenuation. J. Appl. Geophys. 109, 233-241.
[15] Kong, D., Peng, Z., 2015. Seismic random noise attenuation using shearlet and total generalized variation. Journal of Geophysics and Engineering 12(2015),1024-1035.
[16] Zhang, J., Wei, Z. H., 2011. A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising. Appl. Math. Model. 35, 25162528.
[17] Zhang, J., Wei, Z. H., 2008. Fractional variational model and algorithm for image denoising. Fourth Int. Confer. Nat. Comput. (ICNC) 5, 524528.
[18] Liu, Y., Pu, Y., Zhou, J., 2010. Design of image denoising filtering based on fractional integral, Journal of Computational Information Systems 6(9), 2839-2847.
[19] Pu, Y. F., Zhou, J. L., Yuan, X., 2010. Fractional differential mask: a fractional differential based approach for multiscale texture enhancement. IEEE Trans. Image Process. 19 (2), 491511.
[20] Zhang, J., Chen, K., 2015. A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution. SIAM J. IMAGING SCIENCES 8(4), 24872518.
[21] Chan, R. H., Lanza, A, Morigi, Sgallari, F., 2013. An adaptive strategy for the restoration of textured images using fractional order regularization, Numer. Math. Theor. Meth. Appl., 6,276-296.
[22] Zhang, J. Wei, Z., Xiao, L., 2013. Adaptive fractional-order multi-scale method for image denoising, Journal of Mathematical Imaging and Vision, 43, pp. 39-49.